In Louisiana, it is imperative that you get a will. If you don't have one, her children could stand to take much of her estate.
Inheritance rules are different for community and separate property. If the decedent had children or other direct descendants, they will inherit the decedent's separate property and the "naked ownership" of her one-half of the community property subject to a surviving spouse's "usufruct." The usufruct lasts until the surviving spouse dies or remarries. The usufruct applies to community property, even as to children of another marriage, and as to forced heirs' portions, if any. For other intestate successions, you have to classify the decedent's property as community or separate in order to identify the heirs.
Community property goes to the surviving spouse if there are no children or direct descendants. One surprise for many spouses upon the death of their loved one is that they inherit no portion of their spouse's community property if there are children in the marriage (called "forced heirs").
For separate property, there are 5 classes of intestate heirs. They inherit in the following order of priority:
2. Parents and siblings (and their descendants)
If there are siblings (or their descendants) and surviving parent(s), the siblings (or their descendants) inherit subject to a joint and successive usufruct in favor of the parent(s).
If there are siblings (or their descendants) and no surviving parents, siblings (or their descendants) inherit free of usufruct
If there are no siblings (or their descendants), the surviving parent(s) inherit.
Note: Check Civil Code art. 892 for rules for half-siblings
3. Surviving spouse if not judicially separated from decedent
4. More remote ascendants (e.g., grandparents, aunts, uncles)
5. More remote collaterals
Relatives in the most favored class inherit to the exclusion of other classes. The nearest relatives in class, determined by counting degrees (a 'degree' is a generation), inherit to the exclusion of more distant relatives in that class. It is helpful to draw a family tree diagram to determine who inherits.